I've been looking for some series where the protagonist's fighting style is basically just copying his opponent's moves.(Not copying like their superpowers or something.) Only one that comes to mind right now is All-rounder Meguru

Something where the main guy wanted to beat his opponent at their own game would work too. Like in Crows the main guy tried to box boxers, grapple grapplers and so forth.

Have you tried medaka box

I'd think that falls under the "Copying superpowers," but I do rather enjoy it. Not what I'm looking for here though

uhm bowling king

Holyland has it somewhat.

I don't know if this counts by Prince of Tennis has a main character who likes to beat his opponents where they are most confident.

Sometimes he uses his opponent's signature moves after only observing them, or serves them a counterattack.

There's also a move he learns later that allows him to use any move he has seen in the past.

________________
I believe that the best mangas are still out there, waiting to be discovered.

Holyland is yeah.
Bowling King... is Bowling King. It does have it.
Ruler of the Land. I do remember him pulling other people's moves.
Yeah, I'd say PoT does count

The main guy in Chocolat(Seinin) does something like this, although it's not really a big part of the series. I think it's from the main girl's perspective alot.

The main guy form Ryuurouden is able to do this.

Oh, and I recently discovered this one: Densetsu no Yuusha no Densetsu
It's only 1 chapter so far, but it fits your category: the ability to copy others' moves.

________________
I believe that the best mangas are still out there, waiting to be discovered.

Air gear has some of it too. Ikki do copy others move..
Rip offs are the best xD